REGULAR PAPER

Japanese Journal of Applied Physics 56, 087202 (2017)https://doi.org/10.7567/JJAP.56.087202

Ejection of small droplet from microplate using focused ultrasoundHiroki Tanaka*, Yosuke Mizuno, and Kentaro Nakamura
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology, Yokohama 226-8503, Japan*E-mail: htanaka@sonic.pi.titech.ac.jp
Received January 19, 2017; accepted May 21, 2017; published online July 25, 2017
We discussed an ultrasonic system for single-droplet ejection from a microplate, which is one of the basic and important procedures in thenoncontact handling of droplets in air. In this system, a 1.5 MHz concave transducer located below the microplate is used for chasing the liquidsurface through a pulse echo method, and also for the ejection of a 1 µL single droplet by the burst of focused ultrasound. We investigated therelationship between the droplet ejection characteristics, the distance from the transducer to the surface of liquid, the material property, and theexcitation condition of the focused ultrasonic transducer. It was veriﬁed that the optimal position of the transducer was off the focal point of soundpressure by +1 mm, because the sound intensity had to be controlled to eject a single droplet. Subsequently, we conﬁrmed experimentally that theejected droplet volume linearly depended on the surface tension of the liquid, and that the droplet volume and ejection velocity were determined by
the Webber number, Reynolds number, and Ohnesolge number. In addition, by optimizing the duration of the burst ultrasound, the droplet volume
and ejection velocity were controlled. © 2017 The Japan Society of Applied Physics

1.

Introduction

The noncontact handling of small components, powders, anddroplets is thought as a key technology in future pharmacy
industry as well as in novel material science and engineering.
Several trials for the noncontact manipulation of object havebeen reported to be based on air pressure1) and magnetic=
electric ﬁelds considering various applications.2,3) Comparedwith these methods, ultrasonic levitation, which is based on
the phenomenon that objects smaller than the wavelength aretrapped at the sound pressure nodal points of the standing
wave ﬁeld, has advantages in tranquility, cost eﬃciency,
and applicability to nonelectric=magnetic objects, and has
attracted considerable attention.4–11) In the meantime, theultrasonic manipulation of small particles or cells in liquid
has been extensively studied by many research groups.12–14)
The authors have set a research goal to implement all theprocedures of noncontact transport of objects, especially droplets, in air based on ultrasonic radiation force, namely, injection, linear transport, direction switching, mixing, ejection,
analysis, and dispensing. We can utilize the kinetic eﬀect ofultrasonic waves in handling small objects in air.15–24) Although the linear transport,25–27) direction switching,28) mixing,29) ejection from the trapped state,30) and dispensing31,32)
have already been demonstrated to some extent, the ejection ofa droplet from a well must be studied to accomplish the goal.
The ejection of a droplet has been researched since 1970s
as “drop-on-demand” or “acoustic drop ejection technology(ADE)”, which was performed by irradiating focused ultrasound to a free liquid surface.33) This technology has beendeveloped also for nozzleless inkjet printing34–37) and liquidhandling in life science.38–42) In these previous researchstudies, the number and volume of droplets were controlled
by adjusting the tone burst of focused ultrasound. The
transfer of nanoliter droplets from one microplate to the otherwas also reported.
In this paper, we discuss a system for droplet ejection fromone of the wells in a microplate. The scheme of transducer
positioning based on liquid surface chasing by a pulse echo
method is proposed. The droplet ejection characteristics ofthe system are evaluated as functions of the distance from thetransducer to the surface of liquid, the material property, andthe excitation condition of the focused ultrasonic transducer.

Fig. 1. (Color online) Ejection system for droplet from microplate.

2.

Droplet ejection system

2.1

Conﬁguration of ejection system
Figure 1 illustrates the ejection system to be discussed in thispaper. A concave transducer with a radius of curvature of
60 mm and an aperture diameter of 30 mm is located below a
microplate, and driven with 1.5 MHz tone-burst waves. The
microplate has 96 wells. The diameter and depth of each well
are 6.8 and 11.0 mm, respectively. The ultrasound waves arefocused at the surface of liquid contained in the well acrossthe bottom of the microplate. The thickness of the bottom
is 1.4 mm. An acrylic pipe is used to support the microplate.
A thin poly(vinyl chloride) (PVC) ﬁlm is set at the top end of
the pipe to conﬁne water inside the pipe.
2.2 Ejection scheme procedure considered in thispaper
The procedure of the droplet ejection system for the
microplate consists of three steps as shown in Fig. 2. In theﬁrst step, the distance from the transducer to the surface ofliquid is estimated by a pulse echo method at room temperature (20–25 °C). The concave transducer for the ejection
is used also for pulse–echo measurement. In the second step,

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H. Tanaka et al.

Fig. 2. (Color online) Schematic procedure of noncontact droplet ejection system.

(a)

(b)

Fig. 3. (Color online) (a) Echo signal received at the transducer positioned 63.5 mm relative to the liquid surface and (b) distance measured from thetransducer to the liquid surface by pulse echo method.

the position of the transducer is adjusted according to theresult of the pulse–echo measurement. In the third step, adroplet is ejected.
2.3 Distance measurement between liquid surface
and transducer
The distance between the liquid surface and the transducer wasmeasured by a pulse echo method from 51.0 to 70.0 mm in
1.0 mm steps. One of the wells of the microplate was ﬁlledwith water. The transducer was driven by a single cycleof sinusoidal voltage of 60 V. Figure 3(a) shows the signal
received by the same transducer when the distance from thetransducer to the surface of liquid was set at 60 mm. The waves
indicated with i, ii, and iii correspond to the driving signal, thereﬂected signals from the bottom of the well, and the surface ofliquid, respectively. The durations of the waves were increasedby the ringing of the transducer due to its resonance. The shortspikes observed between these ultrasound signals are thought
to be attributed to electrical reﬂections in the cable. The time
between the driving signal and the reﬂected signal from thesurface was measured as the time-of-ﬂight (ToF) by zerocrossing detection. Using the ToF, the distance D (from thetransducer to the surface of liquid) was calculated as
Cw ToF
Cw
D¼
þ 1
d;
ð1Þ
2
Cp
considering the thickness of the microplate bottom, d. The
microplate is made of polystyrene. Here, Cw and Cp are thesound speeds in water and polystyrene, respectively. Cw, Cp,
and d are 1500 m=s, 2340 m=s, and 1.45 mm, respectively. The
distance measured by the pulse echo method is plotted as theactual distance as shown in Fig. 3(b). The distance from thetransducer to the surface of liquid was successfully estimatedover the whole range considered. The amplitude of the pulse
reﬂected from the liquid surface was measured along thecentral axis of the transducer as shown in Fig. 4(a). The squareof the envelope amplitude is plotted as the normalized soundintensity in the ﬁgure. The blue line indicates the normalized
theoretical sound intensity calculated from the sound pressurepðt; rÞ at the distance r on the transducer central axis:43)
pðt; rÞ
 



8
R0
r
R
>
>
u t
c
u t
>
>
>
Cw
Cw
R0  r
>
>
>

< 2 
a
R0
¼
 t
>
2R0
Cw
>
>
>
 



>
>
R0
R
r
>
>
u t
u t
: c
Cw
Cw
R0  r(r < R0 )(r ¼ R0 ) :(r > R0 )ð2ÞHere, R0 is the radius of curvature of the transducer, a is thetransducer aperture radius, and u(t) and α(t) represent thevibration velocity and acceleration of the transducer, respectively. Continuous sinusoidal waves are applied for u(t) andα(t). Note that the focal point of sound intensity exists at the087202-2© 2017 The Japan Society of Applied Physics

H. Tanaka et al.

Sound intensity [arb. unit]

Jpn. J. Appl. Phys. 56, 087202 (2017)(a)Fig. 5. (Color online) Experimental images of droplet ejection taken withshutter speed of 1=20,000 s and frame rate of 2,000 fps.

(b)Fig. 4. (Color online) Sound intensity distribution along (a) the axis of thetransducer and (b) transverse direction from the center across the focal
position.

distance of r ∼ 58 mm, which is smaller than the geometrical
focal length R0 = 60 mm. The sound intensity of 50% of thatat the focal point is reserved for ±5 mm in front and at theback of the focus. Subsequently, we measured the transverse
distribution of sound intensity in the focal area. A thin opticalﬁber needle hydrophone for detecting the reﬂectivity change at
the ﬁber end according to the sound pressure44–46) was used.
The measured sound intensity is shown in red in Fig. 4(b),while the distribution given by the following approximate
equation47) is drawn using a blue line.
pðÞ /

J1 ðka sin Þka sin ð3ÞHere, k is the wave number (= 2π=λ) and J1 is the Bessel
function of the ﬁrst kind. Most of the acoustic power is
conﬁned in the area with a diameter of 3–4 mm, which is
suﬃciently smaller than the diameter of the well. The position
drift of the ﬁber end due to the circulation of the water inducedby acoustic streaming might cause measurement error.
3.
3.1

Ejection of droplet

Trajectory of droplet
Figure 5 shows the images of the ejection of a water droplet
taken using a high-speed camera with a frame rate of 2,000
fps (frames per second) and a shutter speed of 1=20,000 s.
The distance between the liquid surface and the transducer
was set at 60 mm, and the duration of excitation was 5 ms.
The time t was measured from the start of surface deformation. As observed in Fig. 5, the area corresponding to thefocused region was deformed, and the acoustic intensity inthis area was estimated to be higher than 12 kW=m2 using themeasured sound intensity. Thus, the acoustic power applied
to the liquid surface was approximately 0.1 W by the contour
integration of the acoustic intensity distribution.
At t = 2.5 ms, part of the liquid surface protrudes steeply
and the protrusion is composed of two round parts. At t =7.5 ms, the ﬁrst part is pinched oﬀ and launched as a droplet.
At t = 10.0 ms, the remaining liquid surface deforms into
two round parts. Figure 6(a) shows the vertical positions of
the centers of the round part and the launched droplet. Bluecircles, red squares, and green triangles represent the centersof the launched droplet and the ﬁrst and second round parts,
respectively. The ﬁrst round part departed at around t = 7.5
ms and continued to ﬂy upward, and the trajectory is plottedin the ﬁgure. As the surface of the droplet was oscillating,
we ﬁtted the shape with an ellipse and recorded its centeras the trace. Before the droplet separated, the wavelength ofliquid surface deformation, which is the distance between
two round parts, was 1 mm, and after the separation, thewavelength became 0.7–2.2 mm. The capillary length κ −1 isdeﬁned as the characteristic length scale for an interface
subject to gravity and surface tension. The surface wave of
ﬂuid can be recognized as the capillary wave if the wavelength is larger than the capillary length (λ ≪ 2πκ −1), otherwise the gravity wave (λ ≫ 2πκ −1). The capillary length κ −1
is deﬁned asrﬃﬃﬃﬃﬃﬃ;ð4Þ 1 ¼
gwhere σ is the surface tension, ρ is the density, and g is
the acceleration of gravity. The wavelengths observed aremuch smaller than 2πκ −1 = 17.1 mm; thus, the wave of theliquid surface is considered as the capillary wave. Figure 6(b)shows the vertical velocities of the ﬁrst (blue) and second
centers after the droplet was pinched oﬀ (red). The maximal
deformation velocity of the surface of liquid was 1.0 m=s, andthe ejection velocity was 0.5 m=s. On average, the liquidsurface deformed at the velocity of 0.68 m=s, and after the
droplet ejection, 0.40 m=s. The phase velocity of the capillarywave, c, can be calculated assﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
g k
c¼
þ ;
ð5Þ
k


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H. Tanaka et al.

(a)

(b)

(b)

Sound intensity [arb. unit](a)Fig. 7. (Color online) (a) Ejection height (red squares, right scale) anddiameter (blue circles, left scale) of droplet, and (b) dependences of soundintensity (blue circles, right scale) and kinetic energy (red squares, left scale)of droplet on distance from transducer to liquid surface.

(c)Fig. 6. (Color online) (a) Vertical positions of ejected droplets (blue)and heights of liquid surfaces of ﬁrst (red) and second centers (green).
(b) Velocities of ﬁrst center (blue) and second center after droplet was
pinched oﬀ (red). (c) Comparison of droplet trajectory measured after thepinching oﬀ (blue) and that calculated from the pinching oﬀ velocity (red).

where k (= 2π=λ) is the wave number. The phase velocities
calculated to be 0.65 and 0.45–0.84 m=s before and after the
droplet separation, respectively, using Eq. (5) with the measured wavelength of the surface wave are in good agreementwith the measured deformation velocities. Thus, the droplet
pinching oﬀ is thought to be caused by, or at least, enhancedby the capillary wave.
Next, we observed the droplet trajectory after the pinching oﬀ and compared it with the theoretical vertical positionh(t):1hðtÞ ¼  gt 2 þ v0 t;2

ð6Þ

where v0 is the pinching-oﬀ velocity of the droplet.
Figure 6(c) shows the measured and calculated trajectories.
The droplet position is estimated from the pinching-oﬀ
velocity using Eq. (6).
3.2 Distance from transducer to liquid surface andejection characteristics
We veriﬁed the relationship between the droplet volume,the ejection height, and the distance from the transducer tothe surface of liquid. The driving voltage and current were
set to 62 V and 6.5 A, respectively. The distance from thetransducer to the surface of liquid was varied from 53.0 to
63.0 mm in 0.1 mm steps. The diameter and velocity ofthe ejected droplet were measured with a high-speed camera.
The ejection height, which is the highest position reached,
was calculated on the basis of the energy conservation law.
The distance from the transducer to the surface of liquid
was measured by the pulse echo method. Figure 7(a) shows
the measured droplet diameter and ejection height. At the
distance of 58 mm, which corresponds to the experimental
focal length, the ejected droplet diameter and ejection heightdecreased. In contrast, at the distances of 57 and 59 mm, thedroplet diameter and ejection height were maximum. This isbecause a very high sound power was irradiated and caused
multiple droplet ejection or nebulizing. The kinetic energyof the droplet was calculated using the measured droplet
diameter and ejection velocity as shown in Fig. 7(b). At
the distances of 57 and 59 mm, the kinetic energy was also
maximum.

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H. Tanaka et al.

(a)

(a)

(b)
(b)
Fig. 8. (Color online) Dependences of (a) ejected water droplet volumeand (b) height on burst duration.

Burst duration and ejection characteristics
Here, we veriﬁed the relationship between the droplet volume,the ejection height, and the duration of the burst ultrasound.
The droplet was ejected ﬁve times with diﬀerent burst
durations of 4.2, 5.0, 7.1, and 10.0 ms with the distance fromthe transducer to the surface of liquid of 60.0 mm. The driving
voltages were 33.0, 29.6, 24.4, and 28.0 V, which were
optimized for the durations of 4.2, 5.0, 7.1, and 10.0 ms,
respectively, so that only a single droplet can be ejected.
If the duration is increased by keeping the driving voltage
constant, the satellite droplets tend to be easily ejected becauseof the increase in irradiated sound pressure. The droplet
diameter and height were measured ﬁve times from the images
taken with a digital video camera. The droplet volume wasestimated using the measured diameter at the peak of its
trajectory, assuming that the droplet is spherical at the peak.
Figures 8(a) and 8(b) show the dependences of the droplet
volume and height on the duration of the ultrasonic irradiation.
When we changed the duration, 0.5–2.0 µL droplets wereejected. As the duration increased, the droplet volume also
increased. At a duration longer than 10 ms, multiple droplets
were likely generated. The ejection height decreased from60 to 30 mm with increasing duration of the burst. Whenthe ejection height was 50 mm, the ejection velocity wasestimated to be around 1 m=s on the basis of the energy
conservation law. Considering that the irradiated acoustic
power to the liquid surface was 0.1 W, the acoustic energy wascalculated as a function of the duration as shown in Fig. 9(a).
The potential energy of the droplet was calculated as shown in
Fig. 9(b) according to the ejected droplet volume and ejection

Fig. 9. (Color online) (a) Dependence of acoustic energy on burst duration and (b) potential energy of ejected droplet (blue circles, left scale) andenergy ratio of potential energy to acoustic energy (red squares, right scale).

3.3

height. As the input acoustic energy increased, the potential
energy of the ejected droplet also increased, in contrast to theenergy ratio. Here, the energy ratio is deﬁned as the ratio of thepotential energy to the acoustic energy.
4.

Material property and ejection characteristics

Next, we studied the dependence of the ejection characteristics on the liquid properties such as surface tension andviscosity. According to the previous research on the falling
droplet from a syringe, the volume Vg is proportional to thesurface tension σ as48)
Vg ¼

2Rs
;
R g

ð7Þ

where Rs is the syringe radius and αR is a function of thesyringe and droplet radii. Thus, we expect that the ejected
droplet volume will also linearly depend on the surface
tension. On the other hand, inkjet characteristics can beevaluated with three dimensionless quantities: We, Weber
number; Re, Reynolds number; Oh, Ohnesorge number;49)

087202-5

v2 L
;

vL
;
Re ¼

pﬃﬃﬃﬃﬃﬃﬃ
We
Oh ¼¼ pﬃﬃﬃﬃﬃﬃﬃﬃ ;
Re
L

We ¼

ð8Þ
ð9Þ
ð10Þ

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Jpn. J. Appl. Phys. 56, 087202 (2017)

H. Tanaka et al.
Table I. Physical properties at 25 °C and experimental results of droplet
ejection.51,52)
Water

Ethanol

Silicone oil

Density ρ (kg=m )

997

789

873

Surface tension σ (mN=m)

72.0

22.0

18.3

Shear viscosity η (mPa s)

0.890

1.08

1.75

Ejection velocity v (m=s)

0.951

0.446

0.896

Droplet diameter d (mm)

1.263

0.733

0.592

Droplet volume V (µL)

1.054

0.206

0.109

3

(a)

(b)

(c)

Fig. 10. (a) Photos of ejected water, (b) ethanol, and (c) silicone oil
droplets taken with shutter speed of 1=10,000 s and frame rate of 1,000 fps.

where v is the velocity of the droplet jet, L is the droplet
diameter, and η is the viscosity of the droplet. The Weber
number (the ratio of the inertial force to the surface tension
force) indicates the stability of the jetting droplet surface;
the Reynolds number (the ratio of the inertial force to theviscous force) indicates the ﬂow pattern of the liquid; theOhnesorge number indicates the ratio of the viscous force tothe square root of the product of the inertia and the surface
tension force. The inkjet characteristics can be estimated byplotting the dependence of the Ohnesorge number on the
Reynolds number in a log–log chart similar to that in Fig. 5of Ref. 50. For example, in the area of Re ≤ 2=Oh, thedroplet has a suﬃcient kinetic energy for ejection. In thearea of Oh Re5=4 ≥ 50, the energy of the droplet is too large
to eject a single droplet, thereby causing multiple droplet
ejection or splashing.50)
We measured the droplet ejection characteristics forthe following three liquids: water, ethanol, and silicone oil.
The viscosity of the silicone oil was 1.75 mPa·s (Shin-Etsu
Silicone KF-96L-2cs). The driving current was set to 1.2 A,
and the distance from the transducer to the surface ofliquid was 60 mm. The ultrasound was irradiated for 5 ms.
The ejected droplet diameter L, volume V, and velocity v were
measured ﬁve times with a high-speed camera. Figures 10(a)–10(c) show the photos of the ejected water, ethanol, andsilicone oil droplets, respectively. Table I shows the material
properties of sample liquids and the measured L, V, and v
averages. It is observed from the photos that the droplet
volume and ejection height decreased as the surface tensionof the liquid decreased. Figure 11 shows the dependence ofthe droplet volume on the surface tension. As expected fromthe previous research on the volume of the droplet falling froma syringe,48) the volume of the ultrasonically ejected droplet
also linearly depends on the surface tension.
To estimate the droplet ejection characteristics, theOhnesorge and Reynolds numbers of water, ethanol, andFig. 11. (Color online) Dependence of ejected droplet volume on surface
tension.

Fig. 12. (Color online) Experimental results plotted in schematic diagramfor drop-on-demand inkjet printing presented in Ref. 50.

silicone oil droplets are plotted in Fig. 5 of Ref. 50, as shownin Fig. 12. The area between the solid and dashed lines indicates the condition for the single droplet ejection according
to the study on inkjet technology. The three results forthe ultrasonic ejection in this study fell in this area. It can beconcluded that the ejection characteristics are also estimatedfrom these thresholds. If we know the surface tension andviscosity of the target liquid, the droplet volume can becontrolled by changing the ejection velocity. In addition,these three results fall in the area of “satellite droplets”,50) andthus it is necessary to control the irradiation time and theamplitude of ultrasound to eject a single droplet.
5.

Conclusions

We investigated the ultrasonic droplet ejection, which is oneof the important procedures used in the noncontact ultrasonicmanipulation of droplets. By irradiating a focused MHz
ultrasound from a place below the bottom of the microplate,

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H. Tanaka et al.

a single droplet was successfully ejected from the liquidsurface in the microplate. Ejection characteristics werediscussed by changing the focusing position. Pulse echomeasurement was introduced to detect the sample surface
position. The relationship between the ejection characteristics
and the liquid properties was investigated. We indicated thatthe droplet volume and ejection velocity can be controlled
by optimizing the duration of burst ultrasound. We believethat these results provide some basic information necessary
to design an ejection system for various sample liquids, andthus realize noncontact ultrasonic transport systems in the
future.
Acknowledgements

This work was supported by JSPS KAKENHI Grant Number
26289054 and a Grant-in-Aid for JSPS Research Fellow
Grant Number 16J07988.

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